Question

find the area of a regular hexagon with an apothem of 5.2 cm and a side length of 6 cm. round to the nearest tenth.

Explanation:

Step1: Recall the perimeter formula

A regular hexagon has 6 equal - side lengths. The perimeter \(P\) of a regular hexagon with side length \(s\) is \(P = 6s\). Given \(s = 6\mathrm{cm}\), then \(P=6\times6 = 36\mathrm{cm}\).

Step2: Recall the area formula for a regular polygon

The area \(A\) of a regular polygon is given by \(A=\frac{1}{2}aP\), where \(a\) is the apothem and \(P\) is the perimeter. Given \(a = 5.2\mathrm{cm}\) and \(P = 36\mathrm{cm}\), then \(A=\frac{1}{2}\times5.2\times36\).

Step3: Calculate the area

First, \(\frac{1}{2}\times5.2 = 2.6\). Then, \(2.6\times36=93.6\mathrm{cm}^{2}\).

Answer:

\(93.6\)